Polar Sets and Relative Dimension for Generalized Brownian Sheet  

作　　者：Hui-qiong Li Zhen-long Chenu 

机构地区：[1]College of Statistics and Mathematics , Zhejiang Gongshang University, Hangzhou 310035, China

出　　处：《Acta Mathematicae Applicatae Sinica》2007年第4期579-592,共14页应用数学学报（英文版）

基　　金：Key Research Base for Humanities and Social Sciences of Zhejiang Provincial High Education Talents(Statistics of Zhejiang Gongshang University)

摘　　要：Let W^～=^～{W^～（t）; t∈ R＋^N） be a d-dimensional N-parameter generalized Brownian sheet. Necessary and sufficient conditions for a compact set E × F to be a polar set for （t,W^～（t）） are proved. It is also proved that if 2N ≤αd, then for any compact set E ∩→ R〉^N,d-2/α Dim E≤inf{dim F：F∈B（R^d）,P{W^～（E）∩F≠0}〉0}≤d-2/βDimE,and if 2N〉αd, then for any compact set F∪→R^d／{0},α/2（d-DimF）≤inf{dimE：E∈B（R〉^N）,P{W^～（E）∩F≠0}〉0}≤β/2（d-DimF）,where B（R^d） and B（R〉^N） denote the Borel σ-algebra in R^d and in R〉^N respectively, dim and Dim are Hausdorff dimension and Packing dimension respectively.Let W^～=^～{W^～（t）; t∈ R＋^N） be a d-dimensional N-parameter generalized Brownian sheet. Necessary and sufficient conditions for a compact set E × F to be a polar set for （t,W^～（t）） are proved. It is also proved that if 2N ≤αd, then for any compact set E ∩→ R〉^N,d-2/α Dim E≤inf{dim F：F∈B（R^d）,P{W^～（E）∩F≠0}〉0}≤d-2/βDimE,and if 2N〉αd, then for any compact set F∪→R^d／{0},α/2（d-DimF）≤inf{dimE：E∈B（R〉^N）,P{W^～（E）∩F≠0}〉0}≤β/2（d-DimF）,where B（R^d） and B（R〉^N） denote the Borel σ-algebra in R^d and in R〉^N respectively, dim and Dim are Hausdorff dimension and Packing dimension respectively.

关 键 词：Generalized Brownian sheet polar set Hausdorff dimension packing dimension 

分 类 号：O24[理学—计算数学]